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Lateral Mixing in the Pycnocline by Baroclinic Mixed Layer Eddies

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Lateral Mixing in the Pycnocline by Baroclinic Mixed Layer Eddies 2080 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 41 Lateral Mixing in the Pycnocline by Baroclinic Mixed Layer Eddies GUALTIERO BADIN Department of Earth Sciences, Boston University, Boston, Massachusetts AMIT TANDON Department of Physics and Department of Estuarine and Ocean Sciences, University of Massachusetts—Dartmouth, North Dartmouth, Massachusetts AMALA MAHADEVAN Department of Earth Sciences, Boston University, Boston, Massachusetts (Manuscript received 10 January 2011, in final form 16 May 2011) ABSTRACT Using a process study model, the effect of mixed layer submesoscale instabilities on the lateral mixing of passive tracers in the pycnocline is explored. Mixed layer eddies that are generated from the baroclinic in- stability of a front within the mixed layer are found to penetrate into the pycnocline leading to an eddying flow field that acts to mix properties laterally along isopycnal surfaces. The mixing of passive tracers released on such isopycnal surfaces is quantified by estimating the variance of the tracer distribution over time. The evolution of the tracer variance reveals that the flow undergoes three different turbulent regimes. The first regime, lasting about 3–4 days (about 5 inertial periods) exhibits near-diffusive behavior; dispersion of the tracer grows nearly linearly with time. In the second regime, which lasts for about 10 days (about 14 inertial periods), tracer dispersion exhibits exponential growth because of the integrated action of high strain rates created by the instabilities. In the third regime, tracer dispersion follows Richardson’s power law. The Nakamura effective diffusivity is used to study the role of individual dynamical filaments in lateral mixing. The filaments, which carry a high concentration of tracer, are characterized by the coincidence of large horizontal strain rate with large vertical vorticity. Within filaments, tracer is sheared without being dispersed, and consequently the effective diffusivity is small in filaments. While the filament centers act as barriers to transport, eddy fluxes are enhanced at the filament edges where gradients are large. 1. Introduction advection of freshwater create lateral gradients in prop- erties. Such horizontal gradients in the temperature and In the oceanic mixed layer (ML), atmospheric forcing, salinity can compensate each other in their contribution ocean dynamics, and their interplay act to leave the to density (Rudnick and Ferrari 1999) or give rise to ML surface waters well mixed. While the ML waters are density fronts. mixed in the vertical, lateral gradients in temperature ML fronts in the ocean are dynamically unstable. They and salinity are a common feature. Processes responsible evolve in response to geostrophic adjustment (Tandon for the creation of lateral gradients in temperature and and Garrett 1994, 1995; Young 1994) while undergoing salinity in the open ocean include nonhomogeneous heat baroclinic instability (Molemaker et al. 2005; Boccaletti and freshwater fluxes, wind mixing associated with the et al. 2007) and frontogenesis (Hoskins and Bretherton passage of a storm, and ocean convection. Near the coast, 1972; Capet et al. 2008a,b). A departure from quasi- the upwelling of deep water, tidal mixing, and estuarine geostrophic dynamics in the ML results in rich submeso- scale dynamics. Frontogenesis, which can be enhanced through interaction with the mesoscale strain field (Bishop Corresponding author address: Gualtiero Badin, Department of Earth Sciences, Boston University, 675 Commonwealth Ave., 1993; McWilliams et al. 2009a,b), is able to transfer energy Boston, MA 02215. from the mesoscale to the small scales where it is dissipated E-mail: [email protected] (Capet et al. 2008c). Fronts give rise to submesoscale DOI: 10.1175/JPO-D-11-05.1 Ó 2011 American Meteorological Society NOVEMBER 2011 B A D I N E T A L . 2081 filaments of intense vertical vorticity with enhanced satellite imagery. We think of this process study as vertical velocities (Spall 1997; Mahadevan and Tandon examining lateral mixing during the growth phase of 2006), which are significant for the transfer of nutrients submesoscale ML instability, which could be viewed to the surface euphotic layer (Levy et al. 2001). The as growing on the edge of an underlying mesoscale ageostrophic secondary circulation that results in verti- feature. cal velocities can be further intensified by vertical mix- In what follows, we present the analysis of numerical ing (Nagai et al. 2006) and nonlinear Ekman effects experiments used to infer tracer mixing that is driven by (Thomas and Lee 2005). The presence of weak stratifi- submesoscale ML eddies generated from various frontal cation and large vertical shears in the ML leads to configurations. In section 2 we also review theoretical ageostrophic baroclinic instabilities (Stone 1966, 1970, results for tracer dispersion and particle statistics that 1971), which have much faster growth rates than baroclinic are useful for understanding tracer dispersion the sub- instability in the pycnocline (Boccaletti et al. 2007). De- mesoscale context. A reader familiar with these could spite being adiabatic, ML baroclinic instability results in skip directly to section 3, which describes our numerical the restratification of the ML (Fox-Kemper et al. 2008). experiments. Our results, in section 4a, start with a de- In contrast to earlier studies that have focused on the scription of submesoscale signatures in the pycnocline role of submesoscale dynamics on vertical advection and arising from surface ML instabilities. To study mixing, we mixing, as well as the rearrangement of buoyancy in the introduce a passive tracer along the initially flat isopycnal ML, the aim of this study is to infer the importance of surfaces at various depths below the ML. As the flow submesoscale dynamics on lateral mixing along isopycnal develops, we use the evolution of the dye distribution to surfaces in the oceanic pycnocline. This is motivated by infer the rate of lateral mixing. Our methods of analysis observations in which rates of lateral mixing were found to are based on previous observational studies where dye be time and scale dependent (Okubo 1970), and the in- was used to infer lateral mixing—for example, during the ferred horizontal diffusivity far exceeded the values that North Atlantic Tracer Release Experiment (NATRE) could be explained by shear dispersion (Sundermeyer and (Ledwell et al. 1998; Sundermeyer and Price 1998; Polzin Price 1998). What are the processes that lead to enhanced and Ferrari 2004) and on the New England continental lateral dispersion on scales of 0.1–10 km? Is such mixing shelf (Houghton 1997; Sundermeyer and Ledwell 2001; driven by dynamical instabilities and thereby associated Ledwell et al. 2004). Since the ML front and geostrophic with the growth and evolution of such instabilities? It has flow field are oriented west to east, and since our model been previously hypothesized that enhanced lateral mix- domain is zonally periodic, we lay down the dye in east– ing in the pycnocline results from the generation of mixed west, x-oriented streaks across the domain, and estimate patches generated by internal wave breaking that spin up dispersion in the cross-front, y direction. We then de- under the action of gravity and rotation to form vortical scribe the time evolution of the tracer concentration modes or eddies (Sundermeyer et al. 2005; Sundermeyer variance for streaks of tracer released on different iso- and Lelong 2005). In this study, we neglect vortical modes, pycnal surfaces in section 4b. We use the variance analysis and instead examine lateral mixing resulting from the to obtain an integrated measure of lateral mixing and as- submesoscale flow field generated by ML eddies. sess its dependence on ML dynamics. The mixing invoked A natural question is to ask whether the submesoscale by this mechanism is compared with values estimated for dynamics of the ML can impact the pycnocline. We ad- other processes in section 4c. In section 4d, we estimate the dress this question with a modeling process study of the effective diffusivity of an individual filament to mechanis- ML and pycnocline within a limited domain (approxi- tically understand the structure and role of submesoscale mately 200 km 3 100 km). Our three-dimensional nu- filaments in mixing. Finally, we present some points of merical ocean model is initialized with a zonally oriented discussion and our conclusions in sections 5 and 6. ML front, overlying an initially quiescent pycnocline with flat isopycnals. The model domain is a zonally periodic channel. The ML is chosen to be deep (;200 m) so as to 2. Theoretical background generate a submesoscale flow field without any forcing. a. ML instabilities The model setup is described in section 3 and in the appendix. The numerical experiments capture the growth In the oceanic ML, ageostrophic baroclinic instability of submesoscale instabilities resulting in the spindown gives rise to dynamical features such as ML eddies of the front. In contrast, oceanic flows are highly developed and submesoscale filaments with typical length scales and most often forced by surface fluxes. Yet, submesoscale (Ls ; 1–10 km) that are much smaller than the Rossby instabilities are frequently triggered on the edges of meso- radius of deformation (Ld ; 10–100 km) associated with scale fronts and meanders as evidenced in high-resolution the pycnocline. Submesoscale dynamics are characterized 2082 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 41 by the Rossby (R0) and Richardson (Ri) numbers at- where H is the initial depth of the ML. It can thus be taining O(1) values locally, where R0 [ z/f is the ratio of seen that the submeso length scale associated with the 21 2 2 the vertical component of relative vorticity z 5 yx 2 uy to inertial time scale ;O( f ) is given by LS ; M H/f . 2 2 2 2 planetary vorticity f,andRi[ N /Uz ,whereUz 5 uz 1 While these scaling arguments apply to the ML, the 2 yz is the square of the vertical shear of the horizontal ve- theory can be extended to estimate the vertical extent of locity (u, y).
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